Equilibrium, chemical redox

The equilibrium (1) at the electrode surface will lie to the right, i.e. the reduction of O will occur if the electrode potential is set at a value more cathodic than E. Conversely, the oxidation of R would require the potential to be more anodic than F/ . Since the potential range in certain solvents can extend from — 3-0 V to + 3-5 V, the driving force for an oxidation or a reduction is of the order of 3 eV or 260 kJ moR and experience shows that this is sufficient for the oxidation and reduction of most organic compounds, including many which are resistant to chemical redox reagents. For example, the electrochemical oxidation of alkanes and alkenes to carbonium ions is possible in several systems... 

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. 

The third largest class of enzymes is the oxidoreductases, which transfer electrons. Oxidoreductase reactions are different from other reactions in that they can be divided into two or more half reactions. Usually there are only two half reactions, but the methane monooxygenase reaction can be divided into three "half reactions." Each chemical half reaction makes an independent contribution to the equilibrium constant E for a chemical redox reaction. For chemical reactions the standard reduction potentials ° can be determined for half reactions by using electrochemical cells, and these measurements have provided most of the information on standard chemical thermodynamic properties of ions. This research has been restricted to rather simple reactions for which electrode reactions are reversible on platinized platinum or other metal electrodes. 

Inner- or outer-sphere surface complex formation is a. necessary prerequisite for most surface chemical redox reactions. (ESR may provide important information regarding the nature of the precursor complex.) When electron transfer is fast k2 ArJArOH]), overall rates of reaction are influenced by rates of organic reductant adsorption. When electron transfer is slow kl < ArJArOH]), Eq. [18] can be modeled as a pseudoequilibrium reaction, using the equilibrium constant... 

Comparing the activation mode of iminium and enamine catalysis, iminium catalysis is based on a LUMO-activation mode of the electrophile whereas enamine catalysis is based on a HOMO-activation of the nucleophile. Keeping in mind the fact that enamine and iminium species are rapidly interconverted via a two-electron redox process (proton abstraction of an iminium species results in an enamine), MacMillan and co-workers reasoned that it should be possible to interrupt this equilibrium chemically by carrying out just a one-electron oxidation of an enamine. This would then generate a three-7i-electron radical cation with a singly occupied molecular orbital (SOMO) that should be activated towards catalytic transfomiatirHis (racemic or asymmetric) not possible using classical enamine or iminium activation (Scheme 80) 316). 

This section addresses colloidal [312] and especially capsular systems, which are not generated by direct self-assembly as encountered for, e.g., vesicles [313]. Therefore, numerous preparation steps are often required, which leads to structures away from the thermodynamic equilibrium (e.g., layer-by-layer assemblies of interpolye-lectrolyte capsules) [314]. Also for capsules, most examples deal with chemical redox-switching instead of electrochemical manipulation ... 

In combination with electrochemical principles, speciation has a long tradition and at least since the last third of the twentieth century this special area skilfully utilises the ability of electroanalysis to indicate the changes in chemical equilibrium and redox state of various substances, which allows— together with determinations of their total content— the identification and quantification of the individual forms and their actual distribution—a problematic deal for many other instrumental techniques. In this respect, specialised teams have elaborated to a remarkable extent mainly the electrochemistry of natural aquatic systems, covering for two decades the dominant part of chemical speciation in environmental electroanalysis (see, e.g., references (15, 16)). 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

Abstract Inorganic polysulfide anions and the related radical anions S play an important role in the redox reactions of elemental sulfur and therefore also in the geobio chemical sulfur cycle. This chapter describes the preparation of the solid polysulfides with up to eight sulfur atoms and univalent cations, as well as their solid state structures, vibrational spectra and their behavior in aqueous and non-aqueous solutions. In addition, the highly colored and reactive radical anions S with n = 2, 3, and 6 are discussed, some of which exist in equilibrium with the corresponding diamagnetic dianions. 

The analysis of thermodynamic data obeying chemical and electrochemical equilibrium is essential in understanding the reactivity of a system to be used for deposition/synthesis of a desired phase prior to moving to experiment and/or implementing complementary kinetic analysis tools. Theoretical and (quasi-)equilibrium data can be summarized in Pourbaix (potential-pH) diagrams, which may provide a comprehensive picture of the electrochemical solution growth system in terms of variables and reaction possibilities under different conditions of pH, redox potential, and/or concentrations of dissolved and electroactive substances. 

Belouzov-Zhabotinsky reaction [12, 13] This chemical reaction is a classical example of non-equilibrium thermodynamics, forming a nonlinear chemical oscillator [14]. Redox-active metal ions with more than one stable oxidation state (e.g., cerium, ruthenium) are reduced by an organic acid (e.g., malonic acid) and re-oxidized by bromate forming temporal or spatial patterns of metal ion concentration in either oxidation state. This is a self-organized structure, because the reaction is not dominated by equilibrium thermodynamic behavior. The reaction is far from equilibrium and remains so for a significant length of time. Finally,... 

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

A redox reaction is a special case of the equilibrium reaction of A + B in Equation 13.1 B is now a reducible group in a biomolecule with an EPR spectrum either in its oxidized or in its reduced state (or both), and A is now an electron or a pair of electrons, that is, reducing equivalents provided by a natural redox partner (a reductive substrate, a coenzyme such as NADH, a protein partner such as cytochrome c), or by a chemical reductant (dithionite), or even by a solid electrode ... 

To model the brine s chemistry, we need to estimate its oxidation state. We could use the ratio of sulfate to sulfide species to fix ao2 > but chemical analysis has not detected reduced sulfur in the brine, which is dominated by sulfate species. A less direct approach is to assume equilibrium with a mineral containing reduced iron or sulfur, or with a pair of minerals that form a redox couple. Equilibrium with hematite and magnetite, for example,... 

The equilibrium model, despite its limitations, in many ways provides a useful if occasionally abstract description of the chemical states of natural waters. However, if used to predict the state of redox reactions, especially at low temperature, the model is likely to fail. This shortcoming does not result from any error in formulating the thermodynamic model. Instead, it arises from the fact that redox reactions in natural waters proceed at such slow rates that they commonly remain far from equilibrium. 

The two reference electrodes and the interface between the two solution are in electronic equilibrium, so that we can express the differences in the inner potential through the differences in the chemical potentials. We denote the chemical potential of the two metal electrodes as hm, those of the two reference systems as / ef and and those of the two redox couples as /u4edox and /ij edox We obtain ... 

A solution of the isolated platinum blue compound usually contains several chemical species described in the previous section. Such complicated behaviors had long been unexplored, but were gradually unveiled as a result of the detailed equilibrium and kinetic studies in recent years. The basic reactions can be classified into four categories (l)HH-HT isomerization (2) redox disproportionation reactions (3) ligand substitution reactions, especially at the axial coordination sites of both Pt(3.0+)2 and Pt(2.5+)4 and (4) redox reactions with coexisting solvents and atmosphere, such as water and 02. In this chapter, reactions 1-4 are summarized. 

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